Collaborative construction of measurement matrix and reconstruction algorithm in compressive sensing

This paper proposes a novel Sensing Dictionary-based Iterative Hard Thresholding (SDIHT) algorithm, which can collaboratively construct the measurement matrix and the reconstruction algorithm in compressive sensing. Pairs of measurement matrix and sensing dictionary are used for compressive projection and designing reconstruction algorithm respectively. The original sparse signal can be recovered exactly until the residual is reduced to zero as iteration proceeds. A sufficient condition for SDIHT algorithm is given and proved. The benefit of SDIHT is its high reconstruction accuracy and low computational complexity. Computer simulation indicates that when the signal sparsity or the measurement number is fixed, SDHIT algorithm can reconstruct 0-1 sparse signal and two dimensional images with better performance and higher efficiency than IHT, OMP and BIHT algorithm can.